Peas in a Pod9
Students will investigate the relationship between the length of a peapod and the number of peas
inside, as well as between the length of a peapod and length across (average size) of the peas, by
collecting and analyzing data. Students will plot their data on a coordinate plane to determine the
correlation between the variables and construct a function to model the linear relationship
between the length of a peapod and the number of peas inside, and length of a peapod and the
average size of a pea.
Suggested Grade Range: 7-9
Approximate Time: 2 hours
State of California Standards:
Mathematics Standards Grade 7: Algebra and Functions
1.0 Students express quantitative relationships by using algebraic terminology,
expressions, equations, inequalities, and graphs.
3.4 Plot the values of quantities whose ratios are always the same (e.g., cost to the
number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the
plot and understand that the slope of the line equals the quantities.
Mathematics Standards Grade 7: Statistics, Data and Probability
1.0 Students collect, organize, and represent data sets that have one or more variables
and identify relationships among variables within a data set by hand and through the use
of an electronic spreadsheet software program:
1.2 Represent two numerical variables on a scatterplot and informally describe how the
data points are distributed and any apparent relationship that exists between the two
variables (e.g., between time spent on homework and grade level).
Mathematics Standards Grades 8-12: Algebra I
7.0 Students verify that a point lies on a line, given an equation of the line. Students are
able to derive linear equations by using the point-slope formula.
Relevant National Standards:
Mathematics Common Core State Standard: 7.EE
B.4 Use variables to represent quantities in a real-world or mathematical problem, and
construct simple equations and inequalities to solve problems by reasoning about the
quantities.
Mathematics Common Core State Standard: 8.F
Use functions to model relationships between quantities:
9
This lesson was adapted and field-tested by Andrea Johnson, Co-Editor.
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4. Construct a function to model a linear relationship between two quantities. Determine
the rate of change and initial value of the function from a description of a relationship or
from two (x, y) values, including reading these from a table or from a graph. Interpret the
rate of change and initial value of a linear function in terms of the situation it models,
and in terms of its graph or a table of values.
Mathematics Common Core State Standards: High School Algebra
CED.A.2. Create equations in two or more variables to represent relationships between
quantities; graph equations on coordinate axes with labels and scales.
Lesson Content Objectives:
 Measure the length of several peapods, count the number of peas inside each, and
measure the length across (diameter) of each pea in each pod. You will calculate the
average size of the peas in each pod using the data you collect.
 Organize the collected data in tables, recognizing that length of a peapod, number of
peas inside, and the average length across a pea are variables in the context of this
lesson.
 Determine the correlation between the variables by creating a scatterplot for the data.
 Construct a function that models the linear relationship between the length of a
peapod and the number of peas inside, and between the length of a peapod and the
average size pea (measured length or diameter).
Materials Needed:
 One copy per student of the “Peas in a Pod” activity sheet
 10 peapods per pair of students (select a wide variety of lengths)
 One ruler per student
 One graphing calculator per student (optional)
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Summary of Lesson Sequence
 Introduce the lesson by leading a discussion about the structure and function of a
peapod to a pea plant. Ask students to make predictions about how many peas are
inside a specific peapod by just looking at it.
 Model a method for accurately measuring the length of a peapod in centimeters then
counting the number of peas in a peapod and organizing the data into a table.
 Model a method for then measuring across (diameter as measured across outside)
each pea, and then finding the average of those lengths.
 Guide students through their practice as they collect data, create scatterplots,
estimating the lines of best fit, and find functions to represent the two sets of data.
 Check for students’ understanding by asking the key questions provided while
students are working on the guided practice.
 Close the lesson by allowing students to compare their results and discuss possible
reasons for any variation among results. Lead students in a discussion of the
relationship between the length of a peapod and the number of peas inside based on
their investigation, as well as the relationship between the length of a peapod and the
average pea size.
Assumed Prior Knowledge
Prior to this lesson students should be able to construct a function based on a graphical
representation of a relationship between two variables. Students should be able to find the
slope of a line from a graph.
Classroom Set Up
Students will work in pairs to collect data by measuring length of a peapod, length
(diameter) of each pea, and counting the number of peas.
Lesson Description
Introduction
Provide one peapod per pair of students to observe. Lead a discussion of the structure and
function of the peapod as a part of a pea plant. Explain:
The peas of a pea plant are the seeds of the plant and are encased in a pod that protects
the seeds during the plant’s development. Peas are technically fruits because they are
seeds that develop from the flower of the plant, but in cooking they are referred to as
vegetables.
Without opening your peapod, can you predict how many peas are inside? [Allow
students to respond by holding up their fingers to respond.]
Without opening your peapod, can you predict the average diameter of the peas?
What characteristic about the peapod may help us predict how many peas are inside?
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Today we will investigate if the length of a peapod is related to the size of the peas or the
number of peas inside. You may already be confident that a longer peapod will contain a
larger number of peas, but we will also consider the average size of the peas to see if
there is a correlation between the length of a peapod and the size of the peas. To do so,
we will be measuring the length of several peapods, then counting the number of peas
inside and measuring the size of each pea.
Model
Use one peapod to model for students an accurate method for measuring the length of a
peapod in centimeters using a ruler. Show how to open the peapod at the seam and count
the number of peas in one pod. Explain that peas that are not fully developed should also
be counted and measured. Demonstrate measuring the length of each pea from a peapod,
while recording the results. Be sure to demonstrate finding the length of the longest
dimension of the pea, since they may not be perfectly round. Explain that students will
repeat this procedure with a partner for their ten peapods.
Guide Students Through Their Practice
Allow students to work in pairs and select at least ten peapods from which to collect data.
As students are measuring and organizing their data in the tables provided on the activity
sheet; walk around the room to check that they are using their ruler to measure accurately
and using centimeter units.
When students have collected data for at least ten peapods, they should create two
scatterplots for their data; one representing the number of peas versus the length of the
pod and one representing the average pea size versus the length of the pod. Ensure that
students are plotting the correct measurements for the x and y values.
Students should then estimate and draw a line that best fits the data for each scatterplot
and determine how the variables correspond (positive, negative, or they do not
correspond).
Guide students through choosing two points on each of their lines to calculate the slopes.
From the slopes, students should construct a function representing the relationship
between the length of the peapod and the number of peas, as well as the length of the
peapod and the average length of the peas.
Check for Understanding
Check for students’ understanding while they are working on the guided practice by
asking the following key questions:
What are the variables in the context of our activity?
How do the variables correspond on your scatterplot?
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Are there any data points that seem to be outliers? Describe the peapod that provided the
outlying data point.
What could help you make a better estimation of the line of best fit?
How can you find the slope of the line of best fit?
Closure
To close the lesson, allow students to share their results and discuss why there are
varying results in the classroom. Ask students: Based on your investigation today,
describe the relationship between the length of a peapod, the number of peas inside, and
the average size of a pea. Using your understanding about the structure and function of
peapods, write why you think a long peapod wouldn’t have a small number of peas or a
short peapod have a large number of peas. How would those situations impact the pea
plant?
Suggestions for Differentiation
 Graphing calculators may be used to find a line of best fit from the scatterplot.
 If students are not yet able to determine a function from a line of best fit, the activity may
be truncated at the point when students create a scatterplot. The discussion would remain
unchanged because students should still be able to recognize the relationship between the
variables from their scatterplot.
 Model for students the format for the table and the scatterplot if necessary.
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Peas in a Pod
Choose ten peapods. Be sure to select some short ones and some long ones.
1. Measure the length of a peapod, then open the peapod and count the peas. Measure length
of each pea and calculate the average size of a pea for each peapod while recording your
data in the table below. Continue to collect data for all ten peapods.
Peapod Length (cm)
EX:
8 cm
Number of Peas
Length Across of Each Pea (cm)
Average Size of Pea (cm)
5
1, 1.2, .9, 1, 1.3
1.08
2. Create two scatterplots for the data you have collected using your table of values.
Peapod Length vs. Number of Peas
Peapod Length vs. Average Pea Size
3. Estimate and draw a line of best fit for each scatterplot using a ruler.
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4. Choose two points on each line to find the slope for each.
Peapod Length vs. Number of Peas Slope:
Peapod Length vs. Average Pea Size Slope:
5. Construct two functions, one representing each line, so that f(x) represents the
relationship between the peapod length and the number of peas and g(x) represents the
relationship between the peapod length and the average pea size.
f(x) =
g(x) =
6. On the back of this page, respond to the following questions:
a. Based on your investigation today, describe the relationship between the length of a
peapod and the number of peas inside, and the length of a peapod and the average pea
size.
b. Using your understanding about the structure and function of peapods, write why you
think a long peapod wouldn’t have a small number of peas or a short peapod have a large
number of peas. How would those situations impact the pea plant?
c. What does the slope represent in each of your functions?
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